the lengths of plate glass parts are measured to the nearest tenth of a millimeter. the lengths are uniformly distributed with values at every tenth of a millimeter starting at 590.1, and continuing through 590.9. determine the mean and variance of the lengths. (a) mean round your answer to two decimal places (e.g. 98.76). (b) variance round your answer to three decimal places (e.g. 98.765)

To factor quadratics with leading coefficients other than 1, you can follow these steps:

Check your factoring by expanding the factored form to see if it simplifies back to the original quadratic equation.

Remember that factoring quadratics with leading coefficients other than 1 may involve more complex algebraic techniques, and in some cases, the quadratic equation may not factor easily. In such cases, you can resort to using the quadratic formula to find the roots of the equation.

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Answer:

(2x + 3)(3x - 7)

Step-by-step explanation:

Factorize 6x² - 5x - 21

Find two numbers which are factors of the product of the coefficient of x² and the constant, and sum to the coefficient of x.  

coefficient of x² mulitplied by the constant = 6 x -21 = -126

So we need to find two numbers that multiply together to make -126 and sum to -5.

Factors of -126 that sum to -5:  9 and -14

As  9 x -14 = -126,  and   9 - 14 = -5

Rewrite the center term of the quadratic as these numbers, so - 5x becomes 9x - 14x:

⇒ 6x² + 9x - 14x - 21

Factorize each pair of terms, checking that the bracket created is the same:

⇒ 3x(2x + 3) - 7(2x + 3)

The first bracket is the common factor of (2x + 3) and the second bracket is the factorized terms outside of each bracket (3x - 7).  So the final factorization is:

(2x + 3)(3x - 7)

Answer:

For each birdhouse built, the cost increases by $3.50

Step-by-step explanation:

Answer:

Step-by-step explanation:

ASA

Answer:

\(C(w) = 5w + 12\)

\(C(w) = 12+5w\)

Step-by-step explanation:

Given information:

- Monthly fee of $12

- $5 fee per workout class

- \(w\) represents the workout classes taken for a month

- - - -

With the given information, we can conclude that \(C(w)=\) workout fee + monthly fee.

Workout fee = \($5w\)

Monthly fee = \($12\)

∴ \(C(w) = 5w + 12\) or \(C(w) = 12+5w\) (they are the same)

Hope this helps :)

According to the solving the distance between two points is:

= 14.77

In coordinate geometry, the distance formula is used to calculate the actual distance between two points. The formula for calculating the distance between two locations (x1,y1) (x 1, y 1) and (x2,y2) (x 2, y 2) is D=(x2x1)2+(y2y1)2 D = (x 2 x 1) 2 + (y 2 y 1) 2.

The length of a line segment seems to be the distance between two locations. Congruent segments are those with the same length. By drawing a line with a ruler, we may compute the approximate distance between two points.

Given points: (-4, 6) and (3, -7)

X₁ = -4
Y₁ = 6
X₂ = 3
Y₂ = -7

We know that the distance between two points:

distance = √((x₂ - x₁)²+(y₂ - y₁)²)

              = √((3 - (-4))²+((-7) - 6)²)

              = √((3 + 4)²+(-13)²)

              = √((7)²+(-13)²)

              = √((49)+(169))

              = √(218)

             = 14.77

According to the solving the distance between two points is:

= 14.77

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Answer: C. domain: {9, 10, 11, 12); range: (22, 32, 41, 30)

Step-by-step explanation:

The data set is:

(9, 22)

(10,32)

(11, 41)

(12, 30).

In the usual notation, the number at the left is the input (belons to the domain) and the number in the right is the output (belongs to the range).

Then the domain would be:

{9, 10, 11, 12}

and the range:

{22, 32, 41, 30}

The correct option is C

Triangle proportionality theorem and the segment addition postulate, indicates that A_F : AT = A_F : 4×A_F, therefore;

A_F : AT = 1 : 4

The triangle proportionality theorem states that a segment drawn in a triangle, such that it is parallel to one side of the triangle and intersects the other two sides at two distinct points, then the proportion in which the segment divides the other two sides are the same.

The specified details of the triangle ΔABC are;

The location of the point D = AB, the location of the point B = AC

The point of intersection of the angle bisector of angle ∠A and DE = F

The point of intersection of the angle bisector of angle ∠A and BC = Point T

AD = 1, DB = 3, AE = 2, EC = 4

Drawing a line CU parallel to DE from point C to intersect AB at U, according to the triangle proportionality theorem, we get;

AE : EC = 2 : 4 = AD : DU = A_F : FV

AD : DU = 1 : 2

A_F : FV = 1 : 2

Therefore; FV = 2 × A_F

FV : VT = DU : BU = 2 : 1

FV = 2 × VT

2 × VT = 2 × A_F by substitution property, therefore;

FV = 2 × A_F

AT = A_F + FV + VT (segment addition postulate)

Therefore; AT = A_F + 2 × A_F + A_F = 4×A_F

A_F : AT = A_F : 4 × A_F = 1 : 4

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Answer:

C≈87.96

r Radius 14

Answer:

809

Step-by-step explanation:

787 susifx

The Z scores a way to standardize and compare data, as well as to identify outliers.

In simple terms, Z bases give information about how far a data point is from the means of the data set in standard deviation units. The original non-standardized heights, on the other hand, did not guarantee this information.

Z scores are used to standardize data and are useful when comparing two or more different data sets. By converting the original data to Z scores, we can compare data that is on different scales or has different units.

For example, suppose we have two data sets: one with heights measured in inches and the other with weights measured in pounds. We cannot compare these data sets directly as they are at different scales. However, by converting them to Z scores, we can compare them on the same scale.

In addition, the obtained Z's provided a way to identify outliers in the data set. Outliers are data points that are unusually far from the means of the data set. Z scores greater than 3 or less than -3 are generally considered outliers.

In general, the obtained bases are a way to standardize and compare data, as well as to identify outliers.

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Answer:

3xy

Step-by-step explanation:

simpled out to

xy+2y/3x

common factor 3xy

3x^2y^2/3xy + 2y^2/3xy

Answer:

LCM = 3xy

Step-by-step explanation:

                         3 | 3xy , 3y

                         x  | xy , y

                         y   | y , y

                                1 , 1

\(LCM = 3 \times x \times y = 3xy\)

Solving :

\(\frac{3}{3xy} + \frac{2y}{3x}\\\\\frac{3}{3xy} + \frac{2y \times x}{3y \times x} \ \ \ \ \ \ [ \ multiply \ and \ divide \ 2nd \ term \ by\ x \ to \ make\ the\ denominators \ same \ ]\\\\\frac{3}{3xy} + \frac{2xy}{3xy}\\\\\frac{3+2xy}{3xy}\)

1. Yearly total dividends paid are $151,250.

2. The dividends per share are $1.25 for common stockholders

3.  The dividends per share are $4 for preferred stockholders.

We must calculate amount of dividends paid to the preferred stockholders in order to get dividends per share for common and preferred stockholders.

The per dividends paid to the preferred stockholders is:

= $50 par value x 8% guaranteed rate of return

= $4 per share

The total dividends paid to preferred stockholders:

=  $4 per share x 5,000 shares

= $20,000

The per dividends paid to those stockholder is calculated as:

= Common stock + Preferred stock

= $1.25 per share + $4 per share

= $5.25 per share

The total dividends paid to common stockholders:

= $5.25 per share x 25,000 shares

= $131,250.

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The horizontal and vertical translations applied to ΔABC:

A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

It is possible to represent linear transformations and solve systems of linear equations using matrices, which are collections of numbers arranged into a predetermined number of rows and columns. A matrix is a rectangular array of letters, numbers, or expressions in mathematics that are arranged in rows and columns. As well as in the sciences like physics, engineering, and economics, matrices are frequently used in computer graphics, image processing, and data analysis. Data manipulation and analysis can be done using well-defined matrix operations like addition, subtraction, multiplication, and inversion.

Given that,

\(\left[\begin{array}{ccc}1&1&4\\4&1&1\\\end{array}\right] + \left[\begin{array}{ccc}-7\\4\end{array}\right] * \left[\begin{array}{ccc}1&1&1\\\\\end{array}\right]\)   = ?

After using matrix operation it can be further solved as,

\(\left[\begin{array}{ccc}5&5&8\\-3&-6&-6\\\end{array}\right]\)

Hence, A horizontal translation of 4 units right and a vertical translation of 7 units down has been applied to ΔABC.

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The range of C(t), the function of the average monthly cost of owning the cell phone, is (60, 560].

The range of a function is the set of all y-values obtained after substituting all possible x-values.

Steps to find the range of a function:

For the given problem:

The price of the device = $500

Monthly plan = $60

C(t) is defined as the average monthly cost of owning the phone.

Let t = number of months of owning the cell phone.

Then, total cost after t month = 500 + 60 t.

Hence, the average is:

C(t) = (500 + 60t)/t

C(t) =  500/t + 60

For t = 1, C(1) = 500 + 60 = 560

For t > 1, C(t) < 560

Therefore the maximum value of C(t) = 560

For t →∞  then 500/t will approach zero, hence:

C(t) →(0 + 60), or C(t) will approach 60.

Therefore, we can conclude that 60 < C(t) ≦ 560, or the range of C(t) is (60, 560].

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False. Different functions cannot have local variables with the same name because each function has its own isolated scope.

In programming, local variables are variables that are declared and used within a specific function. They are only accessible within that function and cannot be accessed or modified by other functions. Local variables are used to store temporary data or intermediate results within the function's scope.

It is important to note that local variables have a limited scope, meaning they are only valid and accessible within the block of code where they are defined. Once the function execution completes, the local variables cease to exist.

Since different functions have their own separate scopes, it is possible to define local variables with the same name in different functions. This is because each function's local variables are independent of each other and do not interfere with one another.

For example, consider two functions, function A and function B. Both functions can have their own local variable named "x" without any conflict or issue. The "x" variable in function A has no connection or impact on the "x" variable in function B. They are distinct and exist within their respective function scopes.

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Different functions can have local variables with the same name without conflict, as they are specific to their function scope. And a group of logically connected statements contributing to the function definition is known as a block.

"True, different functions can have local variables with the same name". Local variables are specific to the function they are declared in and are not known to other functions. Hence, similar names can be used in different function scopes without any conflict.

A set of statements that belong together as a group and contribute to the function definition is known as a block. In programming, a block is a set of logically grouped statements, enclosed in curly braces ' { }'. For instance, the set of statements within a function or a loop or a decision control structure (like if, switch) forms a block.

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Answer:

Step-by-step explanation:

Answer:

Easy

Step-by-step explanation:

4m a second so 40 seconds cause4 x 10

Answer:

im not sure

1398100 meter

Step-by-step explanation:

4+4^(2)+4^(3)+4^(4)+4^(5)

+4^(6)+4^(7)+4^(8)+4^(9)

+4^(10)=1398100

if x = -1 and y= -3

y= 2x-1

-3=2(-1)-1

-3= -2-1

-3= -3

if x=0and y = -1

y=2x-1

-1=2(0)-1

-1=0-1

-1= -1

if x=1 and y=1

y=2x-1

1=2(1)-1

1=2-1

1=1

if x=2 and y=3

y=2x-1

3=2(2)-1

3=4-1

3=3

SO IT'S CORRECT ❤

THANJ YOU

The match can be scheduled in 900 different ways.

Here, the number of players from each school = 3.

Let us assue that the players of the first school be A, B, and C.

And the players of the second school be X, Y, and Z.

Here, each player from the first school has to play twice with each player from the second school.

We can organize the schedule into six different rounds, i.e.,

R1 : AX BY CZ

R2 : AX BZ CY

R3 : AY BX CZ

R4 : AY BZ CX

R5 : AZ BX CY

R6 : AZ BY CX

So, the number of possible ways to do this would be : 6! = 720 ways.

Now, three rounds are played simultaneously in each round.

R1 : AX BZ CY

R2 : AX BZ CY

R3 : AY BX CZ

R4 : AY BX CZ

R5 : AZ BY CX

R6 : AZ BY CX

And R1 : AX BY CZ

R2 : AX BY CZ

R3 : AY BZ CX

R4 : AY BZ CX

R5 : AZ BX CY

R6 : AZ BX CY

The total number of possible ways for the second case would be twice of  6! / (2! 2! 2!), which is equal to 90+ 90 = 180.

Therefore, the total number of ways in which the match can be scheduled is 720 + 180 = 900.

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The complete question is:

central high school is competing against northern high school in a backgammon match. each school has three players, and the contest rules require that each player play two games against each of the other school's players. the match takes place in six rounds, with three games played simultaneously in each round. in how many different ways can the match be scheduled?

The inputs that are solutions for the inequality are:

x = 2

x= 1

Here we have the following inequality:

-5x < 2

We want to see which of the given inputs is a solution for this.

First we can isolate the variable in our inequality, so we get:

-5x < 2

-2 < 5x

-2/5 < x

-0.4 < x

So any value larger than -0.4 is a solution, from the given options, the two that are solutions are:

x = 1

x = 2.

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Answer:

answer is 60,000+3,000+600+10+2

The domain of a function is the set of numbers that can go into a given function.

The set of input values (x) for which a function generates an output value is known as the domain of the function (y).

we can write \(y = f(x).\)

domain is the full set of x-values that can be plugged into a function to produce a y-value.

The most effective approach to finding a domain will depend on the type of function.

The domain is expressed using an open bracket or parenthesis, the domain's two endpoints separated by a comma, and then a closed bracket or parenthesis.

To find domain of function we should know the property of that function like what the function can take inside it.

Like if we consider square root function \(\sqrt{x}\) so inside root negative numbers are not allowed so value of x should be positive means x>=0

So domain of square root function [0, ∞).

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The simplifed form is :A 3y(2x+1)/ x(x+2) 3y times the quantity 2x plus 1 over x times the quantity x plus 2.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

Given;

15xy²/(x² + 5x +6) ÷ ((5x²y/(2x²+7x+3))

We can factorize expressions;

x² + 5x +6 = (x+2)(x+3)

2x²+7x+3  =(2x+1)(x+3)

Therefore we have;

15xy²/(x+2)(x+3) ÷ (5x²y/(2x+1)(x+3))

we can multiply with the reciprocal;

15xy²/(x+2)(x+3) × ((2x+1)(x+3))/5x²y

By Simplifying;

3y/(x+2) × (2x+1)/x

We get; 3y(2x+1)/ x(x+2)

= 3y(2x+1)/ x(x+2)

The answer is :A 3y(2x+1)/ x(x+2) 3y times the quantity 2x plus 1 over x times the quantity x plus 2.

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Answer:

Step-by-step explanation:

answer is b

Answer:

Step-by-step explanation:

You want an equation for the length of fence, its derivative, its critical numbers, and the values of the field dimensions for a rectangular area of 6M square feet that is x feet long and y feet wide with a dividing fence that is also y-feet long. The dimensions minimize the fence length.

The field is rectangular with one side being x and the other being y. The area is ...

  Area = x·y = 6×10⁶

The total length of fence is ...

  F(x, y) = 2x +3y

Using the area relation we can write y in terms of x:

  y = 6×10⁶/x

So, the length of fence required is given by the function ...

  F(x) = 2x + 3(6×10⁶/x)

  F(x) = 2x + 18×10⁶/x

The derivative can be found using the power rule. It is ...

  F'(x) = 2 -18×10⁶/x²

The critical numbers are the values of x that make the derivative undefined or zero. With x in the denominator, the derivative will be undefined when x=0.

Solving F'(x) = 0, we have ...

  0 = 2 - 18×10⁶/x²

  18×10⁶ = 2x² . . . . . multiply by x², add 18×10⁶

  9×10⁶ = x² . . . . . . divide by 2

  ±3000 = x . . . . . . square root

The critical numbers are {-3000, 0, 3000}.

The length of fence is minimized when x = 3000 and y = 6×10⁶/3000 = 2000.

The field is 2000 ft by 3000 ft.

__

Additional comment

You will note that the total lengths of fence in the x- and y-directions are the same. They are both 6000 feet, half the total length of fence required. This is the generic solution to this sort of cost minimizing problem.

For this single-partition case, the long side is x = √(3A/2) for area A. In general, the x dimension is √(Ny/Nx·A) where Nx and Ny are the numbers of fence segments in each direction. This remains true if one side has no fence segment because a "river" or "barn" is used as the barrier.

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Answer:

27p - 9q + 27

Step-by-step explanation:

3(7p - 3q + 9) ← multiply each term in the parenthesis by the 3

= 21p - 9q + 27

Answer:

They are equal if that’s what you’re asking

Step-by-step explanation:

Answer:

A equation with 24 as an answer would be 6*4

Step-by-step explanation: